One aspect of being a horn player that fascinates me is the acoustics of how the things work.

I have a couple of questions for the group.

  1. Split/missed notes; what is actually happening when we try to "start up" a horn on a high note?

    If we do it well we produce from thin air - say - a high F (for example Bruckner 4 opening solo) and if things go wrong a different note appears. I have pondered the theory that to "start up" a horn on a high harmonic we have to pass through all the others to get to it and if our lips are not stimulating the correct frequency through the correct tension, air pressure etc, it results in a missed note being produced.

  2. Tuning notes; how is it possible - in physics terms - to change the pitch produced by a set length of horn by adjusting lip tension ? how do our lips drive the horn away from its resonant frequency ?
Split/missed notes; what is actually happening when we try to "start up" a horn on a high note?

You can buzz just about any pitch you want on your mouthpiece, because it exhibits no real resonances in the normal playing range.

You could also buzz any arbitrary pitch on 'horn' made from an infinitely long piece of tubing.

When you start a note on a real horn, at first the instrument does look like an infinitely long tube to the sound waves produced by your lip. This sound wave travels down the tube at around 345 meters per second, and then reflects off the bell flair and your hand. A small amount of the sound energy leaks out into the room, but most returns back up the tube.

Not until this wave returns do your lips get to find out if they are playing an actual note on the horn, or just some arbitrary pitch. If they are vibrating at one of the overtone resonances of the horn, then the returning sound wave will be timed to help their vibration. But if they are out of phase, it will work against them - and tend to push you towards the nearest resonant note.

So if your initial attack comes at slightly the wrong frequency, people will hear whatever pitch you are buzzing for an instant before the sound reflects back to your lips. Then there will be several round-trip times worth of audible arguments between your lips and the horn (and that can take a while on the F side). Finally, the horn wins, and a nice tone results - hopefully on the overtone you desired, but possibly on an undesired one that was accoustically closer to the pitch you started at.

Why can you bend notes? Your lips are actually quite massive in comparison to the energy contained in the sound waves they produce. With skill and effort, you can continue to fight against out-of-phase reflections, and perhaps wrestle the horn to a draw, thus acheiving some intermediate pitch between what the horns wants and what your lips would produce if they were free buzzing.

For more information, check out Arthur Benade's books: Fundamentals of Musical Acoustics [Buy this book from Amazon.com] if you can find it, or Horns, Strings, and Harmony [Buy this book from Amazon.com] for a less technical approach.

Tuning notes; how is it possible - in physics terms - to change the pitch produced by a set length of horn by adjusting lip tension ? how do our lips drive the horn away from its resonant frequency ?

As I understand it, the length of the vibrating air column in a horn is not the same as the physical length of the tube because the bell flare generates a "virtual tube end" somewhere beyond the bell. The position of this virtual tube end is not fixed so that there is no single resonant frequency for the horn, although the instrument construction means that certain positions are favoured. The resonator in a horn is our lips, and when we adjust lip tension we actually move the virtual tube end to adapt the resonant frequency to the lip frequency. If the actual tube end position coincides with a position favoured by the horn construction, the note is centred. There are limits to how much the virtual tube end will move, so as you lip further away from a note centre, you reach a point where you flip over to the next closest frequency, which is why it is so hard to do a smooth glissando on a non-trombone.

I'm not a physicist and I may be wrong, but then someone on the list will probably put me right.

This sound wave travels down the tube at around 345 meters per second, and then reflects off the bell flair and your hand.

Is this really true for an open tube? (It's easier if we think of an ideal straight tube to begin with, since the bell introduces all sorts of complications.) For a *closed* tube, yes: there will be a node at the closed end and the sound must be reflected back down the tube, escaping wherever there is an air outlet. But for an *open* tube, I've always thought of it as generating a one-directional standing wave with an antinode at the open end, driven by the vibration of the resonator and amplified by sideways reflection from the walls of the tube. I can't really see how the wave will be reflected from the open end. In the real horn, of course, there will be reflections from valves, bends, joints and right hand, but these must almost be regarded as defects rather than essential features. (Remember that trumpeters, trombonists and tubaists eliminate the right-hand reflection, and think of what happens if they use a mute that really does reflect the sound back down the tube.)

So in my model, an open tube resonates best at a frequency determined by the node-at-the-lips/antinode-at-the-open-end distance. You can bend the pitch because the resonance is *nearly* as good even when the antinode is slightly inside or slightly outside the open end - most of the cross-sectional area will still be vibrating. I think the horn works roughly as an open tube with the antinode beyond the bell (alternatively a closed tube with the node some way into the horn - a fundamental frequency of about 120 for concert Bb corresponds to a wavelength of a bit more than 3 m).

When you try to hit a high note on the horn, you try to buzz at the right frequency, i.e. at the pitch you are trying to hit. For the first 0.1 seconds or so, while the start of the wave is travelling down the horn, it doesn't "know" if this is a resonant frequency or not. But once the wave has reached the end of the tube, the conditions are established and the wave resonates for better or worse according to how close you were. So I believe a good horn-player will truly start at the right frequency, and not pass through all the other harmonics as Terry suggested.

The minor fact that you can quote reference works suggests that you may well be far more qualified to preach on this subject than I am. I would be interested to hear what you have to say about my ideas - take it as honest discussion, not criticism of your contribution.

[ ... ] Your hand basically catches those high notes and deflects them back into the horn - which is why the horn works so much higher in its overtone series than the other brass instruments, and why hand position is more critical in the upper register.

But you can play high notes on the horn without the hand. Tony Halstead showed me how to improve my high notes by placing my hand flat to the inside of the bell, thus constricting the opening less. What makes the horn work in the higher overtone range is mainly the small mouthpiece, helped by the narrow bore of the lead pipe. If you adapted a horn mouthpiece to a bass tuba by fitting a tapered lead pipe, you could make it produce sounds in the usual horn register.

[ ... ] But a horn actually has one closed end - your lips almost completely block it. A cylindrical tube the length of a horn will not produce the harmonic series you want. Instead, it will overblow only on odd overtones somewhat like a clarinet, meaning that the 1st interval is not an octave, but an octave and a half.

The common parlance, that closed pipes produce only the odd overtones, is useful for indicating the reason for the relationship of the resonant frequencies, since one can analyse the closed pipe of constant cross-section as half an open pipe of twice the length with a node at the centre. However, when considering the design of a musical instrument, this way of thinking can mislead. If you were to make an oboe of rubber so that you could gradually distort its shape from conical to parallel while blowing it, the ratio of the frequencies of the first two modes of vibration would gradually change from 2 to 3 so, in a certain sense, the octave on the oboe corresponds to the twelfth on the clarinet. The horn consists of a mixture of tapered and parallel bore so adjusted that the modes give harmonically related frequencies in the ratios 2:3:4:5:6 etc. However, making a tapered lead pipe and flared bell combine with a parallel middle section to give the same acoustic effect as the plain conical alpenhorn is a bit of a trick which works best when the length of parallel tubing is somewhere near the middle of the range (about F on the usual double horn in F/Bb). For lesser amounts of parallel tubing, the overall flare is excessive and the overtone series becomes compressed, while for extra amounts the characteristics of the instrument move in the direction of the straight tube and the overtone series expands. This is why low notes on the Bb horn tend to be sharp. Of course we bring them into tune with hand and lip and are scarcely conscious of the effect most of the time, but playing to a frequency meter in the middle of the note with a constant hand position will show it clearly. The converse effect, that low notes on the C and B basso horns (1+3 and 1+2+3 on the F horn) are flat, is compensated by the combination tubing length being slightly too small.

[ re hosepipe horns ] But it if the flair is even greater - like a horn, the fundamental will rise to almost that of an both-ends-open tube, dropping right into place as an in-tune pedal note an octave below the 1st overtone.

According to Benade (it may have been in a Scientific American article called "Physics of Brasses") the true fundamental of horns is about a third flat. Pedal notes are in tune because second and third harmonics of the lip motion lock into the second and third resonances of the tube. The fundamental being a different frequency probably contributes to the instability of these notes: on both the open Bb of my Bb and F alto Alexander and on my natural horn crooked in Bb alto, there are good pedal Bbs which (with lip alone) I can easily push down to Ab, with difficulty to G, and no further.

As an exercise, play 3rd space C on the F horn. Draw the corners FORWARD until the note slips over to a D.

No problem so far.

Now go back and increase the velosity of the air. It should do the same thing.

This is the part I'm not convinced about. If I do this, and ensure that my embouchure doesn't tighten (and I ensure I don't increase pressure) then I just get a louder C. If, however, I think D then it slips over but I'm sure the very act of thinking D causes a tightening. (I will admit that I think less tightening is needed than in the first part.)

If you are correct then it must be that whilst increasing air velocity and not thinking D, I am in fact relaxing my embouchure to maintain a C but I can't feel this happening. If increasing air can change the note then it should, I think, also happen with whistling but here again all that happens is a louder note.

Am I totally mistaken or is my embouchure/breathing different?

I would be interested to know if there is scientific evidence (or a theoretical basis) for increased air velocity alone increasing the pitch. It would seem to me that it's rather like expecting the pitch of a violin string to rise when the bow moves faster.

I send this with some feeling of trepidation since it might be construed as gross heresy, but I am genuinely puzzled.

Having thought about this subject and read the descriptions of different models put forward to describe what's going on I'm ready for more !!

Effective horn length:

The effective horn length (the length that is involved in the resonance of the note being considered) starts slightly inside the mouth - my thoughts as follows; imagine a 3m/9ft long rope stretched between two points, in order to resonate it without using to much energy I hold it 6 inches along from the end and cultivate the fundamental resonant frequency (each end still, and the middle moving) If I try to cultivate resonance from the fixed end nothing will happen, in this model we have to put energy into the resonator from within the resonators length.

Now, apply this model to the horn, our lips vibrate and they are part way down the resonating tube, this position could be variable - I would speculate that two things control this, one - our lip muscles, two - the air chamber inside the lips which could include mouth, throat, lungs etc. This variance could contribute to our ability to drive a horn away from its resonant frequency.

The bell end of the horn has been described best I think by Richard Merewether and I rehash briefly his model: The horn behaves as a quarter length resonator (the fundamental tone is four times the horns length) the combination of a horn bell flair and a well placed hand make the effective length change with pitch, the low notes effectively end deep in the bell, and as the pitch goes up this end point move towards the hand reaching it at about high G on the F slide.

Now the clever bit is that the quarter tone generator produces an even harmonics series which do not reinforce each other and by changing the effective length of the horn we shrink these into being an odd harmonic series which does reinforce itself, therefore when we play one note all the others can be present at a lower amplitude and it is these that give the horn its magnificent tone. Just think when four horns on open F slides play a C major chord how rich the chord is, now just imagine all the harmonics from all the horns interacting and reinforcing each other, you can feel this happening with your lips being exposed to the reflections traveling into the horn and your hand on the bell as it picks up the other players notes.

Starting up a horn:

When we start up a horn on a high note what happens ? Try this model:

Our lips are still, the air column is still, then we tense our muscles, blow and pop a series of packets of air into the horn, they come out at a particular rate and each one is at a high air pressure compared to the outside air, by controlling the air pressure we control the sound volume, by controlling the rate of packets released we control the pitch (frequency).

Now these pressure packets start traveling down the tube, when the first one gets to the end the horn starts to sound at the pitch we want BUT as it reaches the end some of the energy is reflected back as a returning pressure packet (this assumes that the end of the tube reflects) this returning packet then keeps hitting the outgoing packets, if they interfere to produce a standing wave than we have a note, if they interfere destructively then we have a split/clamp/flubb. With a standing wave which extends slightly past our lips we can make it go louder or quieter, higher or lower, all with lip control.

Driving the horn off it resonant frequency:

I can see two possible models for this:

Using the "lips within the effective tube length" model we may be able to alter how far along the virtual tube our lips are thus altering the length and the resonant frequency.

Or we can force the horn off its resonant frequency a little, I suspect that this results in a more limited amplitude (we can only do this at lowish volumes) and that the resonance of other harmonics is disrupted (this will make the tone less rich/intense)

If anybody has got this far without hitting the Delete key thank you for reading my efforts. I must thank Charles Turner, Chris Stratton, Howard Gilbert, Francis Markey, and Bob Marsteller for giving me new perspectives on horn acoustics.

  1. He wanted to know where the nodal points are in a horn, so that he could clamp the tubing or put braces in those places.

    The positions of these points depends on the frequency of the note you are playing, so your question annot be answered. Besides, it is not clear that clamping the tubing would have much effect. It would make the tubing a little more rigid; but the tubing is already pretty rigid.

  2. Where are the nodal points within reach of the hand?

    Well,now you have to tell me what you mean by the expression "nodal" point. It turns out the the open end of a tube is a PRESSURE NODE and it is a displacement antinode. This means the the pressure doesn't vary much, but you have a maximum in the displacements of the oscillating air. So let's assume you mean a pressure node. Then you have to deal with the fact that the actual end of the horn and the effective end are in different places. Basically, the effective end of the horn is closest to your hand at high frequencies, say starting around high G.

    Now tell me this: what is the point of "reaching" a node with your hand?

  3. According to my sources, the speed of sound in carbon dioxide is 23% lower than the speed of sound in air at the same temperature. So if your horn were filled with carbon dioxide, along with your lungs, the the frequencies you play would be 23% lower. My guess is that if half the gas in your horn and lungs were carbon dioxide, then the speed of sound would be 11 or 12% lower than usual. These decreases in speed yield proportional decreases in the frequency of the horn. A quarter stop lowers the frequency by 2.8%. This would happen if your lungs and the horn contained 12% carbon dioxide. (Algebraic details on request.)

    I have occasionally played horn after breathing helium. This causes the playing frequencies to rise. Never do this with your horn unless you have padded ceilings in your house. I have also studied the effect of filling a Whoopee Cushion with helium, but you didn't ask about that.

  4. Will the density of air change whether the horn acts as a half-length or a quarter-length resonator?
    No, these aspects (neither of which is a precise description of horn behavior) depend only on the shape of the air column. Of course, if the density of air is sufficiently low, you don't have sound any more. It is strange how few marching bands perform on the moon, considering how beneficial the vacuum is to the acoustical output of these orgaizations.
  5. Would low density air make high notes easier?

    I don't know. When you blow out through your lips, the emerging air makes forces on the lips and sets them into oscillation. If air density were less, then the air would likely makes smaller forces on the lips. So this might make it a little harder to play. When a high pressure puff goes down the horn, reflects from the bell, and returns to your lips, it makes a force on the lips that controls the frequency. But this force depends on the amplitude of the pressure puff, not on the density of the air.

    At any rate, your idea of going mountain climbing just so you can play high notes may be misguided. But I recall that several listmembers have performed the Long Call in the Andes, so maybe they can answer this.

Howard Gilbert wrote at length that when he attempted to move from C to D on the F horn by increasing air velocity, that he achieved a louder C, and his lips opened somewhat.

Therein lies the rub. Differentiating between air velocity and air volume. Farkas, Jacobs et al discovered that a given note at a given decibel level requires the same amount of air pressure (velocity), measured with an anemometer inside the mouth, on all brass instruments. Higher notes require higher air pressure, whereas lower notes require greater air volume. How can you raise air velocity without increasing air volume? Two ways: control the size of the aperture (embouchure opening) and control the size of the air stream. Farkas experimented with controlling the air stream with the glottis. A less tension-provoking method is to control it with the position of the tongue: low "ah" for low register, high "ee" for upper register.

All of these methods are interrelated, and should be used in conjunction with one another. My separating them was only for demonstration purposes.

The effective horn length (the length that is involved in the resonance of the note being considered) starts slightly inside the mouth - my thoughts as follows; imagine a 3m/9ft long rope stretched between two points, in order to resonate it without using to much energy I hold it 6 inches along from the end and cultivate the fundamental resonant frequency (each end still, and the middle moving) If I try to cultivate resonance from the fixed end nothing will happen, in this model we have to put energy into the resonator from within the resonators length.

Whilst this is true of the rope, I can't see why energy shouldn't be put in at the end of a resonating air column; I am remembering elementary physics experiments where a vibrating tuning fork is placed at the end of a glass cylinder and water run our until resonance is achieved.

On the other hand, if we look at instruments where the mouth cavity cannot be involved eg transverse flute and organ pipe we see the point of energy input IS within the resonator. In addition I remember reading (about 10 years ago) and article which suggested that the baroque period trumpet players used the oral cavity to get extra notes. Just because energy can be put in at the end (I think?) doesn't mean necessarily that it is in the case of the horn.

Now, apply this model to the horn, our lips vibrate and they are part way down the resonating tube, this position could be variable - I would speculate that two things control this, one - our lip muscles, two - the air chamber inside the lips which could include mouth, throat, lungs etc. This variance could contribute to our ability to drive a horn away from its resonant frequency.

This suggests that varying the tongue position while playing is more related to changing the oral cavity volume than, the usual reason given, of changing air speed although it will do that also. I don't think much of the lungs would be involved; if I remember correctly the bronchia quickly branch into very narrow tubes.

What part does the constriction in the mouthpiece play in this model?

I've always heard the the horn is a half length resonator (the fundamental tone is 2 times the effective horn length). Do the calculation yourself: Start with A at 440 cycles per second (fourth space written E treble clef). Then go down three and a half octaves to get to the fundamental tone. Divide the speed of sound (1090 feet/sec) by this number to wind up with 25 feet, a little over twice the 12 foot length of the open F horn. Therefore, the horn is a half length resonator.

With the basic horn physics out of the way, we can procede with some more interesting aspects. Without solving the problems let me just pose a few interesting problems for horn physics students. (Answers not supplied):

  1. Where are the best nodal points along the tubing that could be strongly clamped, braced, or patched to strengthen harmonic vibrations?
  2. Approximately where are the nodal points within reach of the right hand inside the bell?
  3. In Lowell Greer's recent interview reprinted on this list he made a passing observation that as our lungs become increasingly full of carbon dioxide the pitch goes down. What concentration of carbon dioxide would it take to drop the pitch by a quarter tone.
  4. A trick question: Would the density of air blown through the horn affect whether the horn is a half length or quarter length resonator?
  5. Would low density air blown through the horn make high notes easier to produce?
I've always heard the the horn is a half length resonator (the fundamental tone is 2 times the effective horn length). Do the calculation yourself: Start with A at 440 cycles per second (fourth space written E treble clef). Then go down three and a half octaves to get to the fundamental tone. Divide the speed of sound (1090 feet/sec) by this number to wind up with 25 feet, a little over twice the 12 foot length of the open F horn. Therefore, the horn is a half length resonator.

No. Because your lips essentially close off the mouthpiece end of the horn, it must operate as a quarter wavelength resonator. However the nature of the flare throughout the instrument (not just the bell) changes the effective resonant frequencies of these modes. The result is an overtone series very, very similar to what you would get by operating a piece of cylindrical tubing of the same length as a half wave (open both ends) resonator - hence the popular misconception that brass instruments operate as half-wave resonators.

Further, the first overtone of the tube (ie, the next note above the fundamental) although it may be twice the fundamental frequency is not produced by half wave oscillation within the tube. Rather it is really a 3/4 wave mode which happens to occur at twice the frequency of the flare-modified 1/4 wave fundamental.

4. A trick question: Would the density of air blown through the horn affect whether the horn is a half length or quarter length resonator?

No, the nature of the resonator depends essentially only on the termination of its ends. Changing the speed of sound by changing the gas in question may change the overtone mode it operates at for any given driving frequency, but the horn remains essentially a quarter-wave resonator in relation to its (new) fundamental pitch.

Harry Bell is correct. The wave length of the lowest F on the piano (our open F horn fundamental) is 25.8 feet, twice the length of the horn. The wave length of C above the staff (concert F) is 1.6 feet.
Harry Bell is correct. The wave length of the lowest F on the piano (our open F horn fundamental) is 25.8 feet, twice the length of the horn. The wave length of C above the staff (concert F) is 1.6 feet.

Not really. The "free space" wavelength in air has these values, but inside a flaring horn variations in the phase velocity of sound make the wave much longer; hence the horn operates on the overtones of a quarter wave resonator.

According to my sources, the speed of sound in carbon dioxide is 23% lower than the speed of sound in air at the same temperature. So if your horn were filled with carbon dioxide, along with your lungs, the the frequencies you play would be 23% lower. My guess is that if half the gas in your horn and lungs were carbon dioxide, then the speed of sound would be 11 or 12% lower than usual. These decreases in speed yield proportional decreases in the frequency of the horn. A quarter stop lowers the frequency by 2.8%. This would happen if your lungs and the horn contained 12% carbon dioxide. (Algebraic details on request.)

The lungs take oxygen and replace it with carbon dioxide and some water. We mostly burn sugars with the proportions C, 2H, O according to an equation like:

CH20 + O2 -> CO2 + H2O,
so in principle each oxygen molecule can be replaced by one CO2. The amount of H2O is not calculable, since it has both other sources (what we drink) and other excretory routes. However, it is a common experience that exhaled breath contains a fair amount of water vapour. Densities of gases are in proportion to their molecular weights, which are:
O2 : 32; N2 : 28; CO2 : 44; H2O : 18
Thus CO2 and H2O in equal molecular numbers have an average molecular weight of 31, very close to that of oxygen. Even if no water vapour were exhaled, the nitrogen (N2), which constitutes over 3/4 of dry air by weight, would be unaffected.

I believe that a proportion of CO2 in the lungs as high as 5% (ie replacing about 1/4 of the oxygen) is very uncomfortable. Of course professional wind instrumentalists become tolerant of higher quantities than the general public.

My conclusion: pitch may be very slightly lowered (or raised because of water vapour) at the end of a long note, but you need to measure the chemical composition of exhaled breath to see how much and in what direction: calculations can't tell you.

1. He wanted to know where the nodal points are in a horn, so that he could clamp the tubing or put braces in those places.

The positions of these points depends on the frequency of the note you are playing, so your question annot be answered. Besides, it is not clear that clamping the tubing would have much effect. It would make the tubing a little more rigid; but the tubing is already pretty rigid.

It seems to me that putting some lead tape or something at the midpoint of the horn's length (about 6 feet in) might be interesting to experiment with. Buttressing this spot would reinforce all even harmonics from 4 up.

2. Where are the nodal points within reach of the hand?

Well,now you have to tell me what you mean by the expression "nodal" point. It turns out the the open end of a tube is a PRESSURE NODE and it is a DISPLACEMENT ANTINODE. This means the the pressure doesn't vary much, but you have a maximum in the displacements of the oscillating air. So let's assume you mean a pressure node. Then you have to deal with the fact that the actual end of the horn and the effective end are in different places. Basically, the effective end of the horn is closest to your hand at high frequencies, say starting around high G.

Now tell me this: what is the point of "reaching" a node with your hand?

The motivation for this question was a follow-up on Chris Leuba's observation that a historic baroque horn had worn lacquer spots deep inside the bell across from the normal hand position (toward the body). He took this as evidence that the horn players of the time touched spots inside the bell in addition to the standard hand positions. Mr. Leuba's other observation was that he could get a very stable, in tune A above the staff with open B flat horn by touching the bell at a certain spot inside the bell.

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